Concurrent Pattern Calculus (CPC) is a minimal calculus whose communication mechanism is based on a powerful form of symmetric pattern unification. However, the richness of patterns and their unification entails some flexibility in the challenge-reply game that underpins bisimulation. This leads to an ordering upon patterns that is used to define the valid replies to a given challenge. Such a theory can be smoothly adapted to accomplish other, less symmetric, forms of pattern matching (e.g. those of Linda, polyadic π-calculus, and π-calculus with polyadic synchronization) without compromising the coincidence of the two equivalences.